Square root of decimal numbers — lesson. Mathematics CBSE, Class 8.

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We can follow the below steps to find out the square root of the decimal numbers.

Step 1: Calculate the square root of the given decimal number without the decimal.

Step 2: Put the decimal point in the obtained number such that it is half that of the original number.

Note:

(i) If the original number contains a double decimal, then the square of that number will be a single decimal.

\(\frac{\text{Number of decimals in the original number}}{2} = \frac{2}{2} = 1\)

(ii) If the original number contains four decimal, then the square of that number will have two decimal.

\(\frac{\text{Number of decimals in the original number}}{2} = \frac{4}{2} = 2\)

Let's see an example to understand this concept clear.

Example:

Calculate the square root of \(1.44\).

Solution:

The given number is \(1.44\).

First, calculate the square root of the given decimal number without the decimal.

We have to write \(144\) as a product of prime factors.

\begin{array}{l} \underline{2 | 144} \\ \underline{2 | 72} \\ \underline{2 | 36} \\ \underline{2 | 18} \\ \underline{3 | 9} \\ \underline{3 | 3} \\ | 1 \end{array}

\(144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3\)

Now, group the prime factors.

\(144 = (2 \times 2) \times (2 \times 2) \times (3 \times 3)\)

Here, no factor is leftover in grouping.

Therefore, the given number is a perfect square.

Now, take one factor commonly from each group.

\(=\) \(2 \times 2 \times 3\)

\(=\) \(12\)

Thus, \(\sqrt{144} = 12\).

Now, put the decimal point in the obtained number such that it is half that of the original number.

The given number has a double decimal so that the answer would be a single decimal.

That is \(1.2\).

Therefore, the square root of a given decimal number is \(1.44\) \(=\) \(1.2\).

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6. Square root of decimal numbers